Synthetic division, and the Remainder and Factor Theorems

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Luz divides x³ − 4x² + 2x + 8 by x − 3 on a worksheet, using synthetic division with 3 in the box. What is the remainder?

   5
2. 2.

   Milo sets up synthetic division in a notebook: (2x³ + x² − 3x − 1) ÷ (x + 2), with -2 in the box. What is the remainder?

   -7
3. 3.

   Noah divides x³ − 5x + 4 by x − 3 in pencil. The synthetic box holds 3. What is the remainder?

   16
4. 4.

   Ren divides x³ + 3x² − 4x + 7 by x − 2 on a worksheet. The synthetic bottom row is 1, 5, 6, 19. Type powers like x^2. What is the quotient?

   x^2 + 5x + 6
5. 5.

   In a notebook, Tala's synthetic division of (2x³ − x² + 5x − 6) ÷ (x + 1) ends with the row 2, -3, 8, -14. What is the quotient?

   2x^2 - 3x + 8
6. 6.

   Zee divides x³ − 2x² − 5x + 9 by x − 3 in pencil and gets the bottom row 1, 1, -2, 3. What is the quotient?

   x^2 + x - 2
7. 7.

   p(x) = x³ − 2x² + 4x + 3. Jun wants the remainder of p(x) ÷ (x − 3) on a worksheet. The remainder is p(3). What is p(3)?

   24
8. 8.

   p(x) = 2x³ + 3x² − 5x + 1. In a notebook, Kira finds the remainder for x + 2 as p(-2). What is p(-2)?

   7
9. 9.

   p(x) = x³ + 4x² − 3x + 2. In pencil, Luz gets the remainder for x − 2 from p(2). What is p(2)?

   20
10. 10.

    On a puzzle card, p(x) = x³ − 3x² + 5x − 4. Milo knows the remainder for x + 3 is p(-3). What is p(-3)?

    -73